1. Field of the Invention
The present invention relates to optical circulators utilized in lightwave communication systems and more particularly to bi-directional optical circulators within which a first subset of two mutually exclusive subsets of signals propagates in a logical clockwise direction and the second subset of the two mutually exclusive subsets of signals propagates in a logical counterclockwise direction opposite to the clockwise direction. The present invention further relates to wavelength division multiplexers and de-multiplexers in lightwave communications systems and, more particularly, to multiplexers and de-multiplexers utilizing bi-directional optical circulators.
2. Description of the Related Art
The optical circulator is a non-reciprocal multi-port device that has some similarities to an optical isolator but is more generally applicable. FIG. 1 illustrates the operation of a generalized four-port optical circulator 100 of the prior art. Light that enters the circulator at port A 102 exits the optical circulator 100 at port B 104. However, light that enters the optical circulator at port B 104 does not travel to port A 102 but instead exits at port C 106. Similarly, light entering the port C 106 exits only at port D 108, and light entering port D 108 exits only at the port A 102. In general, given a set of n equivalent optical input/output ports comprising a certain logical sequence within an optical circulator, light inputted to any port is outputted from the logical next port in the sequence and is prevented from being output from any other port. Since a light signal will only travel only one way through any two consecutive ports of an optical circulator, such ports, in effect, comprise an optical isolator. By installing a reflector at one port of a generalized n-port optical circulator (where nxe2x89xa74) such that light outputted from the port is reflected back into the same port, the circulator may then be utilized as an (nxe2x88x921)-port circulator. Furthermore, by blocking or failing to utilize one port of a generalized n-port optical circulator (where nxe2x89xa74), the device may be used as an (nxe2x88x921)-port quasi-circulator.
The main application of optical circulators is in bi-directional optical fiber communications in which two signals at the same wavelength may simultaneously propagate in opposite directions through a single fiber. In this way, optical circulators permit a doubling of the bit carrying capacity of an existing unidirectional fiber optic communication link since optical circulators can permit full duplex communication on a single fiber optic link.
FIG. 2 illustrates a common method by which a pair of conventional optical circulators can be used to provide simultaneous, bi-directional communication on a single fiber optic link. Two three-port optical circulators, 110 and 112, are installed at opposite ends of a fiber optic link 114. Each circulator comprises three ports, with ports A1116; B1118 and C1120 located on circulator 110 and ports A2122, B2124 and C2126 located on circulator 112. For optical circulators 111 and 112, communication transmitters 128 and 130 are optically coupled to port A1116 and A2122, respectively, the common fiber link 114 is optically coupled to port B1118 and B2124, respectively, and communication receivers 132 and 134 are optically coupled to port C1120 and port C2126, respectively. Because of the signal light re-direction properties of the optical circulators discussed above, light emitted from each transmitter 128 and 130 is launched into the fiber link 114 from opposite ports B1118 and B2124 in opposite directions. At the end of each respective path, the two optical circulators 110, 112 separate incoming signals from outgoing signals, so that the transmitters 128, 130 and receivers 132, 134 do not interfere with each other.
A more complex bi-directional optical communications system using a star architecture and optical circulators located, together with other components, on customers"" premises, is disclosed in U.S. Pat. No. 5,572,612, which is incorporated herein by reference.
Optical circulators have many other applications in fiber optic communications systems. FIG. 3 illustrates an apparatus disclosed in U.S. Pat. No. 5,822,095 in which an optical add/drop multiplexer is constructed using two optical circulators and an intervening optical filter. U.S. Pat. No. 5,822,095 is incorporated herein by reference.
In FIG. 3 herein, which corresponds to FIG. 1 of U.S. Pat. No. 5,822,095, the wavelength components xcex1 to xcexn, of an input n-wave signal are received by an input optical fiber 136 and transmitted through an optical circulator 138 and an optical fiber 140 to an optical bandpass filter 144. The bandpass filter 144 allows a specific wavelength xcex1 to pass but rejects the other wavelengths xcex2 to xcexn. The rejected wavelengths are reflected by the bandpass filter 144 back to circulator 138 which re-directs them to output fiber 146. Meanwhile, the signal at wavelength xcex1 passes through filter 144 to another optical fiber 148 and thenceforth into another optical circulator 150 which then drops it to an output optical fiber 152. Furthermore, another signal component with the same wavelength xcex1 is simultaneously added and is introduced from another input optical fiber 154 interfaced to the second optical circulator 150. The second optical circulator 150 directs the added second signal to the bandpass filter 144 in the reverse direction from that of the dropped signal. After the second signal with wavelength xcex1 passes through the bandpass filter 144, it is mixed with the rejected wavelengths xcex2 to xcexn from the first input fiber at the first optical circulator 138 and is outputted, along with these other rejected wavelengths, via output fiber 146.
In U.S. Pat. Nos. 5,383,686 and 5,825,520, which are both incorporated herein by reference, optical wavelength multiplexers and de-multiplexers are disclosed in which one or more Bragg grating reflectors are used in conjunction with one or more optical circulators. An example of one such de-multiplexer 155 and multiplexer 157, as disclosed in U.S. Pat. No. 5,825,520, is illustrated herein in FIGS. 4a and 4b, respectively. FIGS. 4a and 4b herein correspond to the FIGS. 3a and 2, respectively, of U.S. Pat. No. 5,825,520, and are explained briefly herein.
In the de-multiplexer 155 of FIG. 4a, an input signal 159 is de-multiplexed into two output signals, 164 and 166. In the multiplexer 157 of FIG. 4b, input signals 167 and 169 are multiplexed into output signals 170.
The grating reflector, such as grating reflector 156 of FIG. 4a or grating reflector 158 of FIG. 4b, typically comprises an in-fiber Bragg grating reflector and specifically reflects only one signal at a specific target wavelength. When coupled to the intermediate port 160 of a three-port optical circulator, such as circulator 162 of FIG. 4a, then only the target wavelength will be returned back to the circulator 162 and thereby directed to the output fiber 164 via port 165 of circulator 162. All other signals at different wavelengths will pass through the grating reflector 156 and then be output via the intermediate port 160 through fiber 166. In this fashion, the target signal is separated from all other signals. In similar fashion, as shown in FIG. 4b, if port 168 is used as input for the signal at wavelength xcexj, port 160 is used as the input for the signal at xcexi, and a grating reflector 158 specific to wavelength xcexj is coupled to port 160, then the two signals are multiplexed and outputted through port 165 to output fiber 170.
As disclosed in U.S. Pat. No. 5,748,349, which is herein incorporated by reference, an optical add/drop multiplexer may be constructed by coupling a plurality of in-fiber Bragg gratings, each targeted to reflect a different wavelength, in series to an intermediate port of one or more optical circulators. An example of one embodiment of the apparatus of U.S. Pat. No. 5,748,349, as shown in FIG. 4 thereof, is shown herein as FIG. 5. To avoid transmitting any optical channel through a radiation mode loss region of any fiber Bragg grating, these gratings are disposed in a grouped sequence, 187 or 208, away from the circulator so as to reflect back to the circulator a sequence of wavelengths, xcex1, xcex2, xcex3, . . . , xcexi, . . . , xcexn in which xcex1 less than xcex2 less than xcex3 less than xcexi less than xcexn.
The prior-art add-drop multiplexer 172 (FIG. 5) comprises a first three-port optical circulator 176 having first circulator port 178, second circulator port 180 and third circulator port 182, and a second three-port optical circulator 198 having first circulator port 200, second circulator port 202, and third circulator port 204. A first optical transmission path 174 optically communicates with first circulator port 178 for carrying a wavelength division multiplexed optical communication signal. A second optical transmission path 184 optically communicates with both the second port 180 of the first optical circulator 176 and the second port 202 of the second optical circulator 198.
Positioned in second optical transmission path 184 are first and second sets of Bragg gratings, respectively 187 and 208, separated by optical isolator 196. The first Bragg grating set 187 includes gratings 188, 190, and 192 respectively corresponding to wavelengths of xcex1, xcex2 and xcex3 where xcex1 less than xcex2 less than xcex3. Optical signals having these wavelengths are reflected back through the second port 180 of circulator 176 and output onto xe2x80x9cdropxe2x80x9d optical transmission path 186. The second Bragg grating set 208 includes gratings 210, 212, and 214 also corresponding to wavelengths of xcex1, xcex2 and xcex3 where xcex less than xcex2 less than xcex3. Optical signals to be added to an optical system are carried by optical transmission path 206 into the first port 200 of the second optical circulator 198 and encounter gratings set 208 when the signals are output onto transmission path 184 through the second port 202 of the second circulator. These xe2x80x9caddxe2x80x9d optical signals are reflected back towards circulator port 202 along with the through optical channels transmitted through first and second gratings sets 187 and 208. The combined optical signals are output through the third port 204 of optical circulator 198 onto optical transmission path 194.
To prevent Fabry-Perot resonances between like gratings on either side of the isolator from leaked optical signals, an isolator 196 is positioned between gratings set 187 and gratings set 208. Isolator 196 permits optical signals to be unidirectional transmitted in the illustrated direction while optical signals propagating in the opposite direction are attenuated.
The reader is referred to U.S. Pat. No. 5,748,349 for further discussion of this and other aspects of the apparatus disclosed therein.
A reduced-ASE light source for fiber optic networks utilizing a circulator and a plurality of fiber Bragg gratings optically coupled in series thereto is disclosed in U.S. Pat. No. 5,812,712, which is herein incorporated by reference. In the apparatus of U.S. Pat. No. 5,812,712, the fiber Bragg gratings reflect only wavelengths corresponding to signal channels back to an intermediate circulator port, whereas unwanted ASE light passes through all the fiber gratings to a non-reflecting termination at which it is eliminated from the system. Wavelengths reflected back to the circulator""s intermediate port by the gratings are directed by the circulator to an output port. In this fashion, light emanating from the output port is essentially free of ASE but has little or no attenuation of the targeted channel wavelengths.
Furthermore, an optical amplifier for use in a WDM system and employing an optical circulator is disclosed in U.S. Pat. No. 5,636,301, which is incorporated herein by reference. In the apparatus disclosed in U.S. Pat. No. 5,636,301, two circulator ports constitute the input and output ports of the amplifier, and a third circulator port is connected to an optically amplifying fiber. Bragg grating reflectors are formed at specific intervals along this fiber chosen such that each WDM channel is reflected back to the circulator at a distance in inverse proportion to the gain per unit length experienced by that channel in the amplifier fiber. In this fashion, the amplifier amplifies all channels to the same extent.
All of the prior art applications using optical circulators have the same limitation-they all use unidirectional optical circulators. In a unidirectional circulator, all wavelength channels are rotated or directed in a certain logical circulation direction (e.g., FIG. 1) around the ports of the device. However, through use of a bi-directional optical circulator, counter-propagating signals may be made to comprise different sets of wavelengths. In a bi-directional optical circulator apparatus, one set of wavelengths propagates in a first logical circulation direction (e.g., clockwise) through the apparatus whereas a second set of wavelengths different from the first propagates in a second logical circulation direction opposite to the first direction. In this fashion, utilization of the bi-directional optical circulator facilitates the development of certain bi-directional optical communication systems.
One example of the wavelength constitution of co-propagating bi-directional signals is illustrated in FIG. 6. In FIG. 6, as an example, the xe2x80x9cbluexe2x80x9d band 601 and the xe2x80x9credxe2x80x9d band 602 occupy separate wavelength regions each wholly contained within the well-known fiber transmission band 603 centered near a wavelength of 1.55 mm. This type of bi-directional lightwave communication scheme is termed xe2x80x9cband bi-directionalxe2x80x9d optical communication herein. In a band bi-directional optical communication system, wavelengths comprising a first band (e.g., the xe2x80x9credxe2x80x9d band of FIG. 6) propagate in a first direction (e.g., eastbound) through the apparatus whereas wavelengths comprising a second band different from the first (e.g., the xe2x80x9cbluexe2x80x9d band of FIG. 6) propagate in a second direction (e.g., westbound) opposite to the first direction. Various types of band bi-directional communication schemes are possible. For instance, the xe2x80x9cbluexe2x80x9d band might correspond to all or a portion of the 1.3 mm fiber transmission band while the xe2x80x9credxe2x80x9d band might correspond to all or a portion of the 1.55 mm transmission band, etc.
FIG. 7 illustrates a more complex form of bi-directional communication, herein termed xe2x80x9cinterleaved bi-directionalxe2x80x9d communication. In interleaved bi-directional communication, every nth channel propagates in one direction along an optical fiber communication system while the remaining channels propagate in the opposite direction. For instance, in FIG. 7, the special case in which n=2 is illustrated in which the even-numbered set of channels 701 denoted by a solid line might comprise the westbound signals and the odd-numbered set of channels 702 denoted by a dashed line might comprise the eastbound channels. Functionally, the set of channels 701 corresponds to the blue channels 601 of FIG. 6 while the set of channels 702 corresponds to the red channels 602. Ideally, within each set of channels 701 or 702, the spacing and widths of the component bands are identical, although this is not required. For instance, in FIG. 7, successive westbound (or eastbound) channels are separated by a frequency spacing of 100 GHz. However, the frequency spacing between a westbound (eastbound) channel and each of the nearest eastbound (westbound) channels is only 50 GHz.
A problem with prior-art circulators as well as of optical devices comprised of such circulators is that band bi-directional and interleaved bi-directional wavelength division multiplexed optical communications are not realizable without an excessive number of components and a complicated architecture. For instance, FIG. 22 illustrates a bi-directional optical add/drop multiplexer architecture for a band bi-directional optical communications system. The prior-art bi-directional optical add/drop multiplexer 2200 utilizes conventional (unidirectional) optical circulators. As described later herein, the add/drop multiplexer 2200 (FIG. 22) both adds and drops wavelengths of a first set of eastbound wavelengths as well as wavelengths of a second set of westbound wavelengths. However, the bi-directional add/drop multiplexer 2200 utilizing conventional circulators 2256-2259 comprises duplicate add/drop systems 2254-2255 which handle eastbound and westbound communications, respectively. Such duplication of systems adds undesirable complexity and cost to the apparatus.
Accordingly, it is an object of the present invention to create such advantages, as described herein, over the prior art through the disclosure of a bi-directional optical circulator.
In view of the above mentioned limitations of conventional unidirectional optical circulators and optical communications systems using such conventional circulators, it is an object of the present invention to provide a method of bi-directional optical circulation wherein, for a plurality of optical input/output ports comprising a certain logical sequence, light of a first set of lights inputted to any port is outputted from the logical next port in the sequence and is prevented from being output from any other port and light of a second set of lights different from the first set inputted to any port is outputted from the logical preceding port in the sequence and is prevented from being output from any other port.
It is a further object of the present invention to provide a bi-directional optical circulator apparatus in both band bi-directional and interleaved bi-directional embodiments.
It is another object of the present invention to provide a set of apparatus and methods related to important applications of bi-directional optical circulators within optical communications systemsxe2x80x94namely, bi-directional wavelength division optical multiplexing, bi-directional wavelength division optical add/drop multiplexing, three-way channel separation, bi-directional optical amplification, two-way multiplexing, and three-way multiplexing.
A bi-directional optical circulator of the present invention is an apparatus that performs the method of bi-directional optical circulation as described above.
Further, a band bi-directional optical circulator of the present invention is an apparatus performing the method in which the first set of lights and the second set of lights comprise separate individually contiguous bands within the wavelength realm. Each such band may comprise one or a plurality of wavelength multiplexed channels wherein each such channel comprises a more-restricted wavelength range and carries an individual signal.
An interleaved bi-directional optical circulator of the present invention is an apparatus performing the method in which the first set of lights and the second set of lights each comprise a plurality of wavelengths wherein the wavelengths comprising the first set and those comprising the second set are interleaved with one another.
Moreover, a signal re-direction mechanism is provided with the present invention and includes a birefringent beam separation plate, two 90xc2x0 optical rotation elements, a birefringent beam recombination plate, a set of two 45xc2x0 optical rotation elements, one being a reciprocal optical rotator and the other being a non-reciprocal optical rotator, a lens and a reflector which provides a means of selectively rotating the polarization of only signals propagating in one direction. The reflector comprises a mirror and waveplate assembly in the band bi-directional embodiment and a non-linear interferometer in the interleaved bi-directional embodiment.
In a preferred embodiment of the present invention, the bi-directional optical circulator of the present invention comprises a ferrule, four optical fibers or ports contained within or secured by the ferrule, four optical collimators disposed adjacent to the optical fibers or ports, a first birefringent walk-off plate disposed adjacent to the collimators and separating unpolarized light input thereto into plane polarized e-ray and e-ray sub-lights, a first and a second 90xc2x0 reciprocal optical rotator disposed adjacent to the first birefringent walk-off plate and opposite to the collimators and each intercepting one of the two sub-lights from each port, a second birefringent walk-off plate disposed adjacent to the two 90xc2x0 optical rotators opposite to the first birefringent plate, a 45xc2x0 reciprocal optical rotator and a 45xc2x0 non-reciprocal optical rotator disposed adjacent to the second birefringent walk-off plate opposite to the two 90xc2x0 reciprocal optical rotators and each intercepting light from two optical ports, a focusing lens disposed adjacent to the two 45xc2x0 optical rotators opposite to the second birefringent plate and a reflecting element disposed at the focal point of the lens opposite to the two 45xc2x0 optical rotators. The reflecting element comprises a mirror and waveplate assembly in the band bi-directional optical circulator and a non-linear interferometer in the interleaved bi-directional optical circulator.
The present invention is also a bi-directional wavelength division optical multiplexer apparatus comprising a three-port bi-directional optical circulator in which two ports are optically coupled to respective bi-directional optical communications systems, each such system comprising a first set of wavelengths propagating in a first direction and a second set of wavelengths different from the first set propagating in a second direction opposite to the first direction, and the third port is optically coupled to a unidirectional or common-wavelength bi-directional optical communication system and further comprising a set of channel-specific reflecting elements disposed within the uni-directional or common-wavelength bi-directional system.
The present invention is also a method for bi-directional optical wavelength division multiplexing in which two bi-directional optical communications systems, each such system comprising a first set of wavelengths propagating in a first direction and a second set of wavelengths different from the first set propagating in a second direction opposite to the first direction, are optically coupled to a single bi-directional optical circulator through a first port and a second port such that the first and second set are input to the circulator through its first and second ports, respectively, and directed in the logical clockwise and counterclockwise direction, respectively, through the circulator to its third port to be output therefrom. The method for bi-directional optical wavelength division multiplexing is further provided such that, after being output from the circulator third port, a first selection of the first wavelength set and a second selection of the second wavelength set are reflected back to and re-input to the circulator at the third port and the first wavelength selection and second wavelength selection are directed in the logical clockwise and counterclockwise direction, respectively, through the circulator to its second port and to its first port, respectively, so as to be output therefrom whilst the non-selected wavelengths are output from the third port.
The present invention is also a bi-directional wavelength division optical add/drop multiplexer apparatus comprising two three-port bi-directional optical circulators optically coupled to one another through one each of their respective ports wherein each circulator is also coupled, via its remaining ports, to a bi-directional optical communication system and a bi-directional optical add/drop system and further comprising a set of channel-specific reflecting elements disposed within the optical coupling between the two three-port bi-directional optical circulators.
The present invention is also a method for bi-directional optical add/drop multiplexing in which a first (second) bi-directional optical transmission system and a first (second) bi-directional optical add/drop system are optically coupled to a first port and a second port of a first of two (second of two) bi-directional optical circulators, wherein each of the first and second bi-directional optical transmission systems and each of the first and second bi-directional optical add/drop systems comprises a first set of wavelengths propagating in a first direction and a second set of wavelengths different from the first set propagating in a second direction opposite to the first direction, such that through-going wavelengths of the first (second) set are directed from the first (second) system to the first port of the first (second) circulator to the third port of the first (second) circulator to the third port of the second (first) circulator to the first port of the second (first) circulator and thence are output to the second (first) system. The method for bi-directional optical add/drop multiplexing is further provided such that dropped wavelengths of the first (second) set are directed from the first (second) system to the first port of the first (second) circulator to the third port of the first (second) circulator back to the third port of the first (second) circulator to the second port of the first (second) circulator and thence are output to the first (second) add/drop line. The method for bi-directional optical add/drop multiplexing is further provided such that added wavelengths of the first (second) set are directed from the second (first) add/drop line to the second port of the second (first) circulator to the third port of the second (first) circulator back to the third port of the second (first) circulator to the first port of the second (first) circulator and thence are output to the second (first) system.
The present invention is also a three-way optical channel separator apparatus comprising a four-port bi-directional optical circulator optically coupled to an input communication system through a first of its ports and to a first output communication system through its logical third port and also coupled to second and third output communication systems through its remaining ports wherein a set of channel-specific reflecting elements is disposed within the second output system and the third output system.
The present invention is also a method for three-way optical channel separation in which a set of wavelengths comprising a first and a second wavelength subset is input to a four-port bi-directional optical circulator through its first port such that the first (second) wavelength set is directed by the circulator in a logical clockwise (counterclockwise) circulation direction to its logical second (fourth) port so as to be output therefrom. The method for three-way optical channel separation is further provided such that, after being output from the circulator second (fourth) port, a first selection of the first wavelength set and a second selection of the second wavelength set are reflected back to and re-input to the circulator at the second (fourth) port and the first wavelength selection of the first set and second wavelength selection of the second set are directed in the logical clockwise (counterclockwise) direction through the circulator to its third port so as to be output therefrom to a first optical output system whilst the non-selected wavelengths of the first (second) set are output from the second (fourth) port to a second (third) optical output system.
The present invention is also a bi-directional optical amplifier apparatus comprising a three-port bi-directional optical circulator optically coupled to two bi-directional optical communications systems through two of its ports and optically coupled to an optical gain element through the third port wherein a dichroic mirror reflecting signal wavelengths and transmitting pump laser wavelengths is disposed at the end of and optically coupled to the end of the optical gain element and wherein a pump laser light is optically coupled to the optical gain element through the dichroic mirror.
The present invention is also a method for bi-directional optical amplification within a bi-directional optical communications system, wherein the system comprises a first set of wavelengths propagating in a first direction and a second set of wavelengths different from the first set propagating in a second direction opposite to the first direction, such that separate segments of the bi-directional system are optically coupled to a single three-port bi-directional optical circulator through its first and second ports so that the first (second) wavelengths input from the first (second) port and are directed through the circulator in a logical clockwise (counterclockwise) direction to the third port so as to be output therefrom to an optical gain element. The method for bi-directional optical amplification is further provided such that the first and second wavelengths propagate through the optical gain element from the third port of the circulator to a dichroic reflector at the end of the optical gain element and back to the third port of the circulator whilst a laser pump beam in inputted to the optical gain element through the dichroic reflector. The method for bi-directional optical amplification is further provided such that the laser pump beam is prevented from entering the optical circulator and such that, after traveling once in each direction through the optical gain element, the first (second) wavelengths are re-input to the circulator through its third port and directed through the circulator in the logical clockwise (counterclockwise) direction to the second (first) port to be output therefrom back to the bi-directional optical communication system.
The present invention is also a two-way wavelength division optical multiplexer apparatus comprising a three port bi-directional optical circulator whose three ports are optically coupled to a first input, a second input and an output optical communication system.
The present invention is also a method for wavelength division optical multiplexing in which a first (second) set of wavelengths are input to a three-port bi-directional optical circulator through its first (second) port and then directed through the circulator in a logical clockwise (counterclockwise) direction to the third port so as to be output therefrom.
The present invention is also a three-way optical multiplexer apparatus comprising a four-port bi-directional optical circulator optically coupled to an input optical communication system through a first of its ports and to an output optical communication system through another port two ports removed from the first port and also coupled to second and third input communication systems through its remaining ports wherein a set of channel-specific reflecting elements is disposed within the second input system and the third input system.
The present invention is also a method for three-way wavelength division optical multiplexing in which a first, second and third set of wavelengths are input to a four-port bi-directional optical circulator through a first, second and third port, respectively and wherein the first (third) wavelengths are all elements of a first (second) subset of wavelengths that are directed through the circulator in a logical clockwise (counterclockwise) circulation direction and wherein the second wavelengths comprise elements of both the first and second wavelength subset. The method for three-way wavelength division optical multiplexing is further provided such that the first (third) wavelengths are directed through the circulator from the first (third) port in a logical clockwise (counterclockwise) circulation direction to the fourth port so as to be output therefrom. The method for three-way wavelength division optical multiplexing is further provided such that the second wavelengths comprising the first (second) wavelength subset are directed through the circulator in a logical clockwise (counterclockwise) circulation direction from the second port to the first (third) port so as to be output therefrom and thence reflected back to and re-input to the circulator through its first (third) port and thence directed in the logical clockwise (counterclockwise) circulation direction to the fourth port so as to be output therefrom.
These together with other objects and advantages which will be subsequently apparent, reside in the details of construction and operation as more fully hereinafter described and claimed, reference being had to the accompanying drawings forming a part hereof, wherein like numerals refer to like parts throughout.